A government sample survey plans to measure the total cholesterol level of an SRS of men aged 20–34.  Suppose that, in fact, the total cholesterol level of all men aged 20–34 follows the Normal distribution with mean μ=182 milligrams per deciliter (mg/dL) and standard deviation σ=37 mg/dL. Use Table A to answer the questions, where necessary.   (a) Choose an SRS of 100 men from this population. What is the sampling distribution of x¯ ? (Use the units of mg/dL.) A) the N(182,0.37) distribution B) the N(182,3.7) distribution C) the N(182,37) distribution D) the N(1.82,0.37) distribution     What is the probability that x¯ takes a value between 180 and 184 mg/dL? This is the probability that x¯ estimates μ within ±2 mg/dL.   A) 0.5400 B) 0.2946 C) 0.7054 D) 0.4108     (b) Choose an SRS of 1000 men from this population. Now what is the probability that x¯ falls within ±2 mg/dL of μ ? (Enter your answer rounded to three decimal places.)   probability=   The larger sample is much more likely to give an accurate estimate of μ.

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.